simulating_a_time-varying_inductor_in_spice
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Simulating a time-varying inductor in Spice
The relationship between the voltage $v_L$ over and the current $i_L$ through an inductor is determined by its inductance $L$:
$$ v_L(t)=L\frac{di_L(t)}{dt}$$
However, this current-voltage relationship is not valid when the inductor is varying in time. For a time variant inductor, the equation modifies to:
$$ v_L(t)=\frac{d}{dt}[L(t).i_L(t)]=L(t)\frac{di_L(t)}{dt}+i_L(t)\frac{dL(t)}{dt}$$
Rearranging this equation gives an expression for the current through the inductor:
$$ i_L(t)=\frac{1}{L(t)}[L(0)i_L(0)+\int_0^t v_L(t) dt $$
valid if $L(t)\neq 0$ at any time.
simulating_a_time-varying_inductor_in_spice.1725866614.txt.gz · Last modified: by bm